We review a few definitions, notations and results of \(\Psi \) -Hilfer fractional derivative [1]}, [2]}.
Let \(\Delta =[a,b]\)  \((0<a<b<\infty )\)  be a finite interval. Consider the space \(C_{1-\zeta ;\,\Psi }(\Delta ,\,\mbox{R})\)  of weighted functions \(h\)  defined on \(\Delta \)  given by
\(C_{1-\zeta ;\, \Psi }(\Delta ,\,\mbox{R}) =\left\lbrace  h:\left( a,b\right]\rightarrow \mathbb {R}~\big |~\left( \Psi \left( t\right) -\Psi \left(a\right) \right) ^{1-\zeta }h\left( t\right) \in C(\Delta ,\,\mbox{R})\right\rbrace  ,\text{ }0< \zeta \le 1\) 
